Equations of Circles

Front

What is the standard form of the equation of a circle?

Back

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the center of a circle from its equation?

Back

To find the center of a circle from its equation in standard form (x - h)² + (y - k)² = r², identify the values of h and k.

Front

What is the radius of a circle if its equation is (x - 1)² + (y + 2)² = 16?

Back

The radius is 4 units, since r² = 16, thus r = √16 = 4.

Front

What is the diameter of a circle if the radius is 5 units?

Back

The diameter is 10 units, since diameter = 2 * radius.

Front

What does the term (h, k) represent in the equation of a circle?

Back

The term (h, k) represents the center of the circle.

Front

How can you convert the general form of a circle's equation to standard form?

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Front

What is the center of the circle given by the equation (x - 3)² + (y + 1)² = 25?

Back

The center is (3, -1).

Front

If a circle has the equation x² + y² = 36, what is its radius?

Back

The radius is 6 units, since r² = 36, thus r = √36 = 6.

Front

What is the relationship between the radius and the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

What does the equation x² + y² = r² represent?

Back

This equation represents a circle centered at the origin (0, 0) with radius r.